Social choice and the mathematics of manipulation
"Honesty in voting, it turns out, is not always the best policy. Indeed, in the early 1970s, Allan Gibbard and Mark Satterthwaite, building on the seminal work of Nobel Laureate Kenneth Arrow, proved that with three or more alternatives there is no reasonable voting system that is non-manipulable; voters will always have an opportunity to benefit by submitting a disingenuous ballot. The ensuing decades produced a number of theorems of striking mathematical naturality that dealt with the manipul…
Read More ↓Title Statements
- Full title :Social choice and the mathematics of manipulation / Alan D. Taylor.
Summary
"Honesty in voting, it turns out, is not always the best policy. Indeed, in the early 1970s, Allan Gibbard and Mark Satterthwaite, building on the seminal work of Nobel Laureate Kenneth Arrow, proved that with three or more alternatives there is no reasonable voting system that is non-manipulable; voters will always have an opportunity to benefit by submitting a disingenuous ballot. The ensuing decades produced a number of theorems of striking mathematical naturality that dealt with the manipulability of voting systems. This book presents many of these results from the last quarter of the twentieth century - especially the contributions of economists and philosophers - from a mathematical point of view, with many new proofs. The presentation is almost completely self-contained and requires no prerequisites except a willingness to follow rigorous mathematical arguments."--Jacket.
Read More ↓Edition Statements
- Publication Date:2005.
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge
- Language:eng
- Publication Date:2005.
Notes
"Mathematical Association of America."
The Physical Object
- Description:xi, 176 pages ; : 24 cm.
Edition Identifiers
- ISBN:0521810523, 9780521810524, 0521008832, 9780521008839
- oclc:ocm55878011
- LC Classification:JF1001
- Dewey Decimal:324.6/01/5193
Table of Contents
An introduction to social choice theory : Some intuitions, terminology, and an example ; A little history ; Arrow’s theorem ; Twenty voting rules ; Exercises -- An introduction to manipulability : Set preferences and manipulability ; Specific examples of manipulation ; Summary of the main results ; Agenda manipulability and transitive rationality ; Exercises -- Resolute voting rules : The Gibbard-Satterthwaite theorem ; Ties in the ballots ; The equivalence of Arrow’s theorem and the Gibbard-Satterthwaite theorem ; Reflections on the proof of the Gibbard-Satterthwaite theorem ; Exercises -- Non-resolute voting rules : The Duggan-Schwartz theorem ; Ties in the ballots ; Feldman’s theorem ; Expected utility results -- Social choice functions : The Barberá-Kelly theorem ; Ties in the ballots ; Another Barberá theorem ; The MacIntyre-Pattanaik theorem -- Ultrafillers and the infinite : The infinite version of Arrow’s theorem ; Infinite Gibbard-Satterthwaite without invisible dictators ; Invisible dictators resurrected ; Infinitely many voters and infinitely many alternatives -- More on resolute procedures : Combinatorial equivalents ; Characterization theorems for resolute voting rule…
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